STRUCTURE OF Er-162, Er-164, Er-166, Er-167, Er-168, Er-170
By Prof Lefteris Kaliambos (Natural Philosopher in New Energy) ( July 2014) Historically the discovery of the assumed uncharged neutron (1932) along with the invalid relativity (EXPERIMENTS REJECT RELATIVITY) led to the abandonment of the well-established electromagnetic laws, in favour of various contradicting nuclear theories, which could not lead to the nuclear structure. Under this physics crisis and using the charged UP and DOWN quarks discovered by Gell-Mann and Zweig I published my paper “Nuclear structure is governed by the fundamental laws of electromagnetism ”(2003), which led to my discovery of the new structure of protons and neutrons given by proton = + 5d + 4u = 288 quarks = mass of 1836.15 electrons neutron = + 4u + 8d = 288 quarks = mass of 1838.68 electrons The paper was also presented at a nuclear conference held at NCSR "Demokritos" (2002). Here one can see the 9 charged quarks in proton and the 12 ones in neutron able to give the charge distributions in nucleons for revealing the strong electromagnetic force for the nuclear binding in the correct nuclear structure by applying the laws of electromagnetism. You can see my papers of nuclear structure in my FUNDAMENTAL PHYSICS CONCEPTS. Note that according to my discovery of the LAW OF ENERGY AND MASS the mass defect in the nuclear structure is due to the photon mass of the emitting dipolic photon presented at the international conference "Frontiers of fundamental physics" (1993) organised by the natural philosophers M. Barone and F. Selleri , who gave me an award including a disc of the atomic philosopher Democritus. Nevertheless today many physicist continue to apply not the well-established laws but the various fallacious nuclear structure models which lead to complications. STRUCTURES OF ERBIUM Naturally occurring erbium (Er) is composed of 6 stable isotopes, Er-162, Er-164, Er-166, Er-167, Er-168, and Er-170 with Er-166 being the most abundant (33.503% natural abundance). Comparing the structures of erbium of 68 protons (even number) with those of Holmium of 67 protons (odd number) we see that the isotopes of erbium have structures of high symmetry, because here the vertical n68p68 replaces the n38p38 of the holmium . (See my STRUCTURE OF Ho-165 ). After a careful analysis of this comparison I discovered that the additional vertical n68p68 form with the p66n66 the symmetrical alpha particle which gives 2(n) of opposite spins. Finally here we have the four symmetrical alpha particles with 8(n). So under these symmetrical arrangements the number N of blank positions is given by The two horizontal squares give 8n of strong bonds with opposite spins. The first and the sixth plane give 4(n) of weak bonds with opposite spins. The second and the fifth plane give 4{n} with three bonds per neutron and 8n. The third and the fourth plane give 4(n) of weak bonds with opposite spins. The four symmetrical alpha particles give at the same planes 8(n) of opposite spins. That is N = 4{n} +16n + 16(n) = 36 blank positions able to receive 18 extra neutrons of positive spins and 18 extra neutrons of negative spins . ' ' STRUCTURE OF Er-162, Er-164, Er-166, Er-168, Er-170 WITH S = 0 Since the 68 protons and 68 neutrons give S=0 we conclude that the S =0 of the above nuclides is due to the total S = 0 of extra neutrons. For example the Er-162 of 26 extra neutrons has 4{n} +16n + 6(n) of opposite spins, while the Er-170 of 34 extra neutrons has 4{n} + 16n + 14(n) of opposite spins. STRUCTURE OF Er-167 WITH S = +7/2 ' '''In this case of odd number of extra neutrons we see that the number of extra neutrons of positive spins is much more greater than the number of negative spins because the p39n39 is moved from the down horizontal square (-HSQ to the up square (+HSQ) in order to fill the blank positions existing in front of p38 n38. So it changes the spin from S = -1 to S =+1. Note that this change of spin gives S =+2. Under this condition the 8(n) of the two previous squares now become 6(n) blank positions of opposite spins. That is, the total number of blank positions is not 36 but 34. Such blank positions are able to receive 17 extra neutrons of positive spins and 17 extra neutrons of negative spins. Since the change of spin gives S = +2 we conclude that the S = +7/2 is due to the total S = +3/2 of the extra neutrons. In other words the Er-167 of 31 extra neutrons has 14 extra neutrons of negative spins and 17 extra neutrons of positive spins which fill just the 17 blank positions of positive spins. That is S = +2 +17(+1/2) +14(-1/2) = +7/2 '''DIAGRAM OF ERBIUM-136 (CORE) FORMING 36 BLANK POSITIONS' This structure of Er-136 (Core) has S =o with six horizontal planes of opposite spins like the +HP1, -HP2, +HP3, -HP4, +HP5, and -HP6 including the two horizontal squares of opposite spins like the -HSQ and +HSQ. Here the additional pn systems as vertical p68n68 ar not shown. But you can see the n68 near the p51 by using the top view of the third plane. Note that the p47n47 along with the p48n48 make in the core two symmetrical alpha particles of opposite spins . But you cannot see the p49n49, the n52p52 of the third alpha particle and the n50p50 and the p51n51 of the fourth alpha particle. Also the p41, n41, p42, n42, p43, n43, p44, and n44 which form the central parallelepiped of opposite spins are not shown. In the same way the 8 deuterons of opposite spins from p13n13 to p20n20 and the 4 deuterons from p33n33 to p36 n36 are not shown. n40......p40........n ' n......... p38.......n38 +HSQ' ' n31………p12.........n12.......p32' ' p31........n11.........p11…… n32 -HP6' ' n........p29.........n10.........p10…… n30 ' ' n29…… p9..........n9 …….p30.........n +HP5 ' ' n61....p47.......n27.........p8..........n8.........p28........... n48......p62' ' p64....n45..........p27........n7.........p7........n28..........p46...........n63 -HP4 ' ' p61......n47..........p25.........n6.........p6..........n26...........p48.....n62' ' n64....p45..........n25…….p5..........n5……….p26.......n46 .........p63 +HP3' ' n23………p4.........n4………….p24..............n' ' n......p23…….....n3………....p3………..n24 -HP2' ' p21.........n2………p2............n22' ' n21........p1........n1.........p22] +HP1' ' n.........p37......n37 ' ' n39......p39........n -HSQ' TOP VIEW OF THE FIRST HORIZONTAL PLANE ' Here you see the 2(n) of weak horizontal bonds ' (n)........p34....... n34 ' p21....... n2........ p2....... n22 ' ' n21.........p1. .......n1.......p22' ' n33.......p33..... (n)' ' TOP VIEW OF THE SECOND HORIZONTAL PLANE' Here we have 2{n} +4n and the same situation occurs at the fifth horizontal plane. ' n' ' n14.......p14........{n}' ' n23.......p4.........n4.........p24..........n ' ' n.......p23........n3........p3.........n24' ' {n}...... p13......n13 ' ' n' ' TOP VIEW OF THE THIRD HORIZONTAL PLANE WITH POSITIVE SPINS ' Here the first 2(n) of horizontal bonds fill the blank positions of the central parallelepiped, while the second 4(n) of horizontal bonds are formed by the additional alpha particles. Using this top view of the third plane you can see the following characteristics of the fundamental shapes formed by the nucleons of the central parallelepiped as The p5n5 and n6p6 create the small horizontal square of Mg-24 for creating the central parallelepiped of the alpha particle nuclei. The n15p15 and p16n16 create the first small horizontal rectangle. The p25n25 and p26n26 create the second small horizontal rectangle. The p41, n42, n43 and p44 make the great horizontal square of the great central parallelepiped. The p45, n46, n47 and p48 form the first great horizontal rectangle. The p49, n50, p51 and n52 form the second great horizontal rectangle. ' ' ' (n)....... p66........n68' ' (n)........p58....... n50.......p51....n60 ' ' (n) p53........n42........p16......n16......p44.......n54' ' p61 n47........p25........n6........p6........n26.......p48 n62' ' n64 p45........n25........p5........n5........p26...... n46 p63 ' ' n55........p41.......n15.......p15.......n43......p56 (n)' ' n57.......p49.......n52......p59........(n)' n65.......p67.......(n) ' ' ' ' TOP WIEW OF THE UP HORIZONTAL SQUARE ' n' ' n40......p40.......n ' ' n.....p38.......n38' ' n' Category:Fundamental physics concepts